First order reaction- If the rate of reaction depends upon the 1st power of the concentration term of reactant is called first order reaction.
Let us consider a reaction
A → B
Initially a 0
After time a-x x
Rate of reaction = (dx/dt) ∝ (a-x)
or, (dx/dt) = k(a-x)
Where, k is rate constant
On rearrangement of above equation we have-
dx/(a-x) = kdt ...(i)
On integration of equation (i) we get-
or, -ln(a-x) = kt + c ...(ii)
Where C is an integration constant If, = 0, then x = 0 Now, putting the value of t and x in (ii) we get ln a = c Now, putting the value of c in equation (ii) we have
ln (a-x) = kt - ln a
or, ln a - ln (a - x) = kt
